5+ Year Member

Can someone plz break this problem down for me & explain it to me in a very basic way. I am very bad at permutations & combination. Thank you!

A jeweler has exactly six distinct beads: 3 agate beads and 3 quartz beads. All the beads are different color. If the jeweler wants to alternate the beads so that no 2 agate or quartz beads are adjacent, in how many different ways could the jeweler string the beads on a single thread?

2+ Year Member

Can someone plz break this problem down for me & explain it to me in a very basic way. I am very bad at permutations & combination. Thank you!

A jeweler has exactly six distinct beads: 3 agate beads and 3 quartz beads. All the beads are different color. If the jeweler wants to alternate the beads so that no 2 agate or quartz beads are adjacent, in how many different ways could the jeweler string the beads on a single thread?

2+ Year Member

The correect answer is 72.
Let's say quartz = q
agate = a
In order to get that order, you gotta have either a,q,a,q,a,q or q,a,q,a,q,a

in the first type: there are 3 possibilites for the 'a' on the left, then 2 for the one in the middle [you subtract one, because they can't repeat], and 1 for the 'a' on the right. The same for q. The one on the left has 3 possibilites, then 2 in the middle, and 1 for the q at the right side.
So we have 3 * 3 * 2 * 2 * 1 * 1 = 36.

for the q,a,q,a,q,a situation, you get another 36 ways by the same procedure as I described.

36 + 36 = 72 total ways to make that necklace or whatever.

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5+ Year Member

The correect answer is 72.
Let's say quartz = q
agate = a
In order to get that order, you gotta have either a,q,a,q,a,q or q,a,q,a,q,a

in the first type: there are 3 possibilites for the 'a' on the left, then 2 for the one in the middle [you subtract one, because they can't repeat], and 1 for the 'a' on the right. The same for q. The one on the left has 3 possibilites, then 2 in the middle, and 1 for the q at the right side.
So we have 3 * 3 * 2 * 2 * 1 * 1 = 36.

for the q,a,q,a,q,a situation, you get another 36 ways by the same procedure as I described.

2+ Year Member

I guess there is only one or at most 2 of these questions on the QR.
Lol, I did a lot of these type of annoying question in my 8th grade in an AP math class, and that is why I'm good at those. You can still get better with reading the practice tests' manual. This one was a bit tough. The chances of getting one similar to the one you just posted is much more. I mean the ones you have a few types of stuff in the bag, and you take out some of them at once. Try to learn that for sure.

Loaded like a freight train
Flyin' like an aeroplane
Feelin' like a space brain

Stop hovering to collapse...Click to collapse...Hover to expand...Click to expand...

5+ Year Member

I guess there is only one or at most 2 of these questions on the QR.
Lol, I did a lot of these type of annoying question in my 8th grade in an AP math class, and that is why I'm good at those. You can still get better with reading the practice tests' manual. This one was a bit tough. The chances of getting one similar to the one you just posted is much more. I mean the ones you have a few types of stuff in the bag, and you take out some of them at once. Try to learn that for sure.

Click to expand...

This was nothing compared to the other ones that kaplan has in their freaking quizzes. It is so annoying when I can't solve a math problem.